English

Symmetry of hypergeometric functions over finite fields and geometric interpretation

Number Theory 2026-04-22 v4

Abstract

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms between certain algebraic varieties. The numbers of rational points on these varieties are hypergeometric functions over finite fields.

Keywords

Cite

@article{arxiv.2505.05858,
  title  = {Symmetry of hypergeometric functions over finite fields and geometric interpretation},
  author = {Akio Nakagawa},
  journal= {arXiv preprint arXiv:2505.05858},
  year   = {2026}
}

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45 pages